Finite Group Databasebeta

← #34099111

Subgroups — #34099111

Order 20096.

238 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 51 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23757902C211yesmaximal, characteristic
2#23757431C211yesmaximal, characteristic
3#23757428C211yesmaximal, characteristic
4#23757194C211yesmaximal, characteristic
5#23757009C211yesmaximal, characteristic
6#23756998C211yesmaximal, characteristic
7#328×C157C211yesmaximal, characteristic
8C22×Dic314C2211yescharacteristic
9C2×Dic628—21no—
10C2×#14578944—21no—
11#19097770—21no—
12#19097769—21no—
13#19097761—21no—
14#19097761—21no—
15#19097750C2211yescharacteristic
16#19097748—21no—
17#19097727—21no—
18C2×C4⋊Dic157—21no—
19C2×#14578933C2211yescharacteristic
20#19097696—21no—
21#19097694—21no—
22C22⋊#11929434C2211yescharacteristic
23#19097678—21no—
24C22⋊Q8×C157C2211yescharacteristic
25C22⋊C8×C157C2211yescharacteristic
26#95×C157C2211yescharacteristic
27C2×Dic314—21no—
28C2×Dic314—21no—
29C2×Dic314—21no—
30C2×Dic314—42no—
31C2×Dic314D411yescharacteristic
32C22×Dic157—21no—
33C22×Dic157D411yescharacteristic
34C22×Dic157D411yescharacteristic
35Dic628—42no—
36#14578944—42no—
37C2×#11929434—21no—
38C4⋊Dic157—21no—
39C4⋊Dic157—42no—
40C4⋊Dic157D411yescharacteristic
41#14578933—21no—
42#14578933—21no—
43#14578933—21no—
44#14578933—21no—
45#14578933—21no—
46#14578933—21no—
47#14578933—21no—
48C22⋊Dic157—21no—
49C4×Dic157—21no—
50C4×Dic157—21no—
51C2×Q8×C157D411yescharacteristic
52C22×C4×C157—21no—
53C22×C4×C157C2311yescharacteristic
54C2×C8×C157—21no—
55C4⋊C4×C157—21no—
56C4⋊C4×C157D411yescharacteristic
57C22⋊C4×C157—21no—
58Dic314—22no—
59Dic314—22no—
60Dic314—41no—
61Dic314—41no—
62Dic314—41no—
63Dic314—81no—
64C2×Dic157—21no—
65C2×Dic157—21no—
66C2×Dic157—22no—
67C2×Dic157—21no—
68C2×Dic157—21no—
69C2×Dic157—21no—
70C2×Dic157—41no—
71C2×Dic157—41no—
72C2×Dic157—41no—
73C2×Dic157Q1612yescomplemented
74#11929434—41no—
75C23×C157C2×D411yescharacteristic
76Q8×C157—41no—
77C2×C4×C157—22no—
78C2×C4×C157—21no—
79C2×C4×C157—21no—
80C2×C4×C157—41no—
81C2×C4×C157—41no—
82C2×C4×C157—41no—
83C2×C4×C157C2×D411yescharacteristic
84C2×C4×C157C2×D411yescharacteristic
85C8×C157—41no—
86C22×C157—21no—
87C22×C157—21no—
88C22×C157#12011yescharacteristic
89C22×C157C2×Q1611yescharacteristic
90C22×C157#13711yescharacteristic
91C4×C157—21no—
92C4×C157—21no—
93C4×C157—42no—
94C4×C157—41no—
95C4×C157—41no—
96Dic157—22no—
97Dic157—41no—
98Dic157—42no—
99Dic157—41no—
100Dic157—41no—
101C2×C157—21no—
102C2×C157—21no—
103C2×C157#45111yescharacteristic
104C2×C157#45611yescharacteristic
105C2×C157B(4,𝔽2)11yescharacteristic
106C157#160511yescharacteristic, complemented, Sylow
107#1605—1571nomaximal, Sylow
108#544—1571no—
109#451—1571no—
110#451—1571no—
111#395—1571no—
112#328—1571no—
113#328D15711yescharacteristic
114#324—1571no—
115C22×Q8—1571no—
116C2×Q16—3141no—
117C2×Q16—3141no—
118C4⋊Q8—3141no—
119C4⋊Q8—3141no—
120#125—3141no—
121#125—3141no—
122C22⋊Q8—3141no—
123C22⋊Q8—1571no—
124C22⋊Q8C2×D15711yescharacteristic
125#117—3141no—
126C2×C4⋊C4—3141no—
127C2×C4⋊C4—1571no—
128#103—3141no—
129#103—3141no—
130C22⋊C8—1571no—
131C22⋊C8C2×D15711yescharacteristic
132#95—3141no—
133#95C2×D15711yescharacteristic
134C2×Q8—3141no—
135C2×Q8—3141no—
136C2×Q8—3141no—
137C2×Q8—6282no—
138C2×Q8—1571no—
139C2×Q8D62811yescharacteristic
140C22×C4—21no—
141C22×C4—3141no—
142C22×C4—1571no—
143C22×C4—1571no—
144C22×C4C22×D15711yescharacteristic
145Q16—6282no—
146Q16—6282no—
147C2×C8—21no—
148C2×C8—3141no—
149C4⋊C4—21no—
150C4⋊C4—3141no—
151C4⋊C4—3141no—
152C4⋊C4—3141no—
153C4⋊C4—3141no—
154C4⋊C4—3141no—
155C4⋊C4—3141no—
156C4⋊C4—3141no—
157C4⋊C4—3141no—
158C4⋊C4—6282no—
159C4⋊C4—1571no—
160C4⋊C4D62811yescharacteristic
161C22⋊C4—21no—
162C22⋊C4—3141no—
163C42—3141no—
164C42—3141no—
165C23D4×D15711yescharacteristic
166Q8—41no—
167Q8—3142no—
168Q8—3142no—
169Q8—6281no—
170Q8—6281no—
171Q8—6281no—
172Q8—12561no—
173C2×C4—22no—
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—41no—
177C2×C4—41no—
178C2×C4—41no—
179C2×C4—3141no—
180C2×C4—3141no—
181C2×C4—3142no—
182C2×C4—3141no—
183C2×C4—3141no—
184C2×C4—3141no—
185C2×C4—6281no—
186C2×C4—6281no—
187C2×C4—6281no—
188C2×C4—1572no—
189C2×C4D4×D15711yescharacteristic
190C2×C4C2×D62811yescharacteristic
191C8—41no—
192C8—6281no—
193C22—21no—
194C22—21no—
195C22#1909774111yescharacteristic
196C22Q16×D15711yescharacteristic
197C22#1909780011yescharacteristic
198C4—21no—
199C4—21no—
200C4—42no—
201C4—41no—
202C4—41no—
203C4—3142no—
204C4—6281no—
205C4—6282no—
206C4—6281no—
207C4—6281no—
208C2—21no—
209C2—21no—
210C2#2375743011yescharacteristic
211C2#2375745711yescharacteristic
212C2#2375746111yescharacteristic
subgroupG/H
centerC22#19097741
commutator, cosocleC22×C4×C157C23
FrattiniC22×C4C22×D157
Fitting#328×C157C2
socleC22×C157#120
prime radicalC23×C157C2×D4
hypercenter#328D157
hypocenterC157#1605
LCSG ▷ C22×C4×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
73. C2×Dic157Q16semidirect
106. C157#1605semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#237579022
#237574312
#237574282
#237571942
#237570092
#237569982
#328×C1572
#1605157